Searching for Balanced S-Boxes with High Nonlinearity, Low Differential Uniformity, and Improved DPA-Resistance

2020 ◽  
pp. 95-106
Author(s):  
Youle Xu ◽  
Qichun Wang
Keyword(s):  
Differential Uniformity ◽  
High Nonlinearity

scholarly journals More Low Differential Uniformity Permutations over F22k with k Odd

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Yue Leng ◽  
Jinyang Chen ◽  
Tao Xie
Keyword(s):  
Block Ciphers ◽  
Algebraic Degree ◽  
Differential Uniformity ◽  
Numerical Examples ◽  
High Nonlinearity ◽  
Substitution Boxes ◽  
Theoretical Results

Permutations with low differential uniformity, high algebraic degree, and high nonlinearity over F22k can be used as the substitution boxes for many block ciphers. In this paper, several classes of low differential uniformity permutations are constructed based on the method of choosing two permutations over F22k to get the desired permutations. The resulted low differential uniformity permutations have high algebraic degrees and nonlinearities simultaneously, which provide more choices for the substitution boxes. Moreover, some numerical examples are provided to show the efficacy of the theoretical results.

scholarly journals Evolving Dynamic S-Boxes Using Fractional-Order Hopfield Neural Network Based Scheme

Entropy ◽  
2020 ◽  
Vol 22 (7) ◽  
pp. 717 ◽  
Author(s):  
Musheer Ahmad ◽  
Eesa Al-Solami
Keyword(s):  
Neural Network ◽  
Fractional Order ◽  
Hopfield Neural Network ◽  
Performance Assessments ◽  
Comparison Analysis ◽  
Differential Uniformity ◽  
High Nonlinearity ◽  
Substitution Boxes ◽  
Strict Avalanche Criterion ◽  
Independence Criterion

Static substitution-boxes in fixed structured block ciphers may make the system vulnerable to cryptanalysis. However, key-dependent dynamic substitution-boxes (S-boxes) assume to improve the security and robustness of the whole cryptosystem. This paper proposes to present the construction of key-dependent dynamic S-boxes having high nonlinearity. The proposed scheme involves the evolution of initially generated S-box for improved nonlinearity based on the fractional-order time-delayed Hopfield neural network. The cryptographic performance of the evolved S-box is assessed by using standard security parameters, including nonlinearity, strict avalanche criterion, bits independence criterion, differential uniformity, linear approximation probability, etc. The proposed scheme is able to evolve an S-box having mean nonlinearity of 111.25, strict avalanche criteria value of 0.5007, and differential uniformity of 10. The performance assessments demonstrate that the proposed scheme and S-box have excellent features, and are thus capable of offering high nonlinearity in the cryptosystem. The comparison analysis further confirms the improved security features of anticipated scheme and S-box, as compared to many existing chaos-based and other S-boxes.

scholarly journals A New Hyperchaotic System-Based Design for Efficient Bijective Substitution-Boxes

Entropy ◽  
2018 ◽  
Vol 20 (7) ◽  
pp. 525 ◽  
Author(s):  
Eesa Al Solami ◽  
Musheer Ahmad ◽  
Christos Volos ◽  
Mohammad Doja ◽  
Mirza Beg
Keyword(s):  
Performance Assessment ◽  
Performance Comparison ◽  
Hyperchaotic System ◽  
Differential Uniformity ◽  
Avalanche Effect ◽  
High Nonlinearity ◽  
Substitution Boxes ◽  
Novel Method ◽  
Box Method ◽  
New Hyperchaotic System

In this paper, we present a novel method to construct cryptographically strong bijective substitution-boxes based on the complicated dynamics of a new hyperchaotic system. The new hyperchaotic system was found to have good characteristics when compared with other systems utilized for S-box construction. The performance assessment of the proposed S-box method was carried out based on criteria, such as high nonlinearity, a good avalanche effect, bit-independent criteria, and low differential uniformity. The proposed method was also analyzed for the batch-generation of 8 × 8 S-boxes. The analyses found that through a proposed purely chaos-based method, an 8 × 8 S-box with a maximum average high nonlinearity of 108.5, or S-boxes with differential uniformity as low as 8, can be retrieved. Moreover, small-sized S-boxes with high nonlinearity and low differential uniformity are also obtainable. A performance comparison of the anticipated method with recent S-box proposals proved its dominance and effectiveness for a strong bijective S-box construction.

scholarly journals Differentially 4-Uniform Permutations with the Best Known Nonlinearity from Butterflies

2017 ◽  
pp. 228-249 ◽  
Author(s):  
Shihui Fu ◽  
Xiutao Feng ◽  
Baofeng Wu
Keyword(s):  
Finite Field ◽  
Open Problem ◽  
Block Ciphers ◽  
Algebraic Degree ◽  
Differential Uniformity ◽  
Almost Perfect Nonlinear ◽  
High Nonlinearity ◽  
Very High ◽  
Lack Of Knowledge

Many block ciphers use permutations defined over the finite field F22k with low differential uniformity, high nonlinearity, and high algebraic degree to provide confusion. Due to the lack of knowledge about the existence of almost perfect nonlinear (APN) permutations over F22k, which have lowest possible differential uniformity, when k > 3, constructions of differentially 4-uniform permutations are usually considered. However, it is also very difficult to construct such permutations together with high nonlinearity; there are very few known families of such functions, which can have the best known nonlinearity and a high algebraic degree. At Crypto’16, Perrin et al. introduced a structure named butterfly, which leads to permutations over F22k with differential uniformity at most 4 and very high algebraic degree when k is odd. It is posed as an open problem in Perrin et al.’s paper and solved by Canteaut et al. that the nonlinearity is equal to 22k−1−2k. In this paper, we extend Perrin et al.’s work and study the functions constructed from butterflies with exponent e = 2i + 1. It turns out that these functions over F22k with odd k have differential uniformity at most 4 and algebraic degree k +1. Moreover, we prove that for any integer i and odd k such that gcd(i, k) = 1, the nonlinearity equality holds, which also gives another solution to the open problem proposed by Perrin et al. This greatly expands the list of differentially 4-uniform permutations with good nonlinearity and hence provides more candidates for the design of block ciphers.

High nonlinearity and low leakage current SnO2 varistor ceramics by co-doping with yttrium and tantalum

2021 ◽  
Vol 285 ◽  
pp. 129120
Author(s):  
Wenxin Liang ◽  
Hongfeng Zhao ◽  
Xiaoji Meng ◽  
Shaohua Fan ◽  
Qingyun Xie
Keyword(s):  
Leakage Current ◽  
Co Doping ◽  
High Nonlinearity ◽  
Low Leakage ◽  
Low Leakage Current

Ellipse Core Based Photonic Crystal Fiber with High Nonlinearity and Higher Numerical Aperture

2020 ◽  
Author(s):  
Khandaker Rafsan Alam ◽  
Shah Md. Salimullah ◽  
Md. Ashadujjaman Shajol ◽  
Md. Jahid Hasan ◽  
Emamul Haque Hridoy ◽  
...  
Keyword(s):  
Photonic Crystal ◽  
Photonic Crystal Fiber ◽  
Numerical Aperture ◽  
Crystal Fiber ◽  
High Nonlinearity

A large birefringence and high nonlinearity liquid crystal photonic crystal fiber with low confinement loss

2021 ◽  
Vol 65 ◽  
pp. 102610
Author(s):  
Xiaodong Zhou ◽  
Erlei Wang ◽  
Qing Han ◽  
Honglei Yuan ◽  
Jia Li
Keyword(s):  
Liquid Crystal ◽  
Photonic Crystal ◽  
Photonic Crystal Fiber ◽  
Confinement Loss ◽  
Crystal Fiber ◽  
High Nonlinearity

scholarly journals A Novel Construction of Dynamic S-box with High Nonlinearity Using Heuristic Evolution

IEEE Access ◽  
2021 ◽  
pp. 1-1
Author(s):  
Amjad Hussain Zahid ◽  
Abdullah M. Iliyasu ◽  
Musheer Ahmad ◽  
Mian Muhammad Umar Shaban ◽  
Muhammad Junaid Arshad ◽  
...  
Keyword(s):  
High Nonlinearity
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